Sink flow deforms the interface between a viscous liquid and air into a tip singularity

In our experiment, an interface between a viscous liquid and air is deformed by a sink flow of constant flow rate to form a sharp tip. Using a microscope, the interface shape is recorded down to a tip size of 1 mu m. The curvature at the tip is controlled by the distance h between the tip and the sink. As a critical distance h(*) is approached, the curvature diverges like 1/(h-h(*))(3) and the tip becomes cone shaped. As the distance to the sink is decreased further, the opening angle of the cone vanishes like h(2). No evidence for air entrainment was found, except when the tip was inside the orifice.